Acoustoelectric amplification in resonant piezoelectric-semiconductor cavities

ABSTRACT

Interaction of acoustic waves in a piezoelectric-semiconductor resonant cavity with the charge carriers in the semiconductor layer can be directed toward amplification of the acoustic waves; such amplification scheme can be applied in building unilateral amplifiers, zero loss filters, oscillators, high detection range circuit-less wireless sensors, isolators, duplexers, circulators and other acoustic devices. An apparatus for acoustoelectric amplification is described. The apparatus includes a semiconductor layer and a thin piezoelectric layer bonded (or deposited) onto the semiconductor layer forming an acoustic cavity. Two or more tethers forming a current conduction path through the semiconductor layer and two or more access pads to silicon are positioned on two ends of the acoustic cavity and configured to inject a DC current in the semiconductor layer.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with Government support under (Grant number ECCS1810143) awarded by the National Science Foundation (NSF). TheGovernment has certain rights in this invention.

BACKGROUND OF THE INVENTION

Various embodiments relate generally to acoustoelectric (AE)amplification systems, methods, devices and computer programs and, morespecifically, relate to AE amplification in lateral-extensionalthin-film piezoelectric-on-silicon (TPoS).

This section is intended to provide a background or context. Thedescription may include concepts that may be pursued, but have notnecessarily been previously conceived or pursued. Unless indicatedotherwise, what is described in this section is not deemed prior art tothe description and claims and is not admitted to be prior art byinclusion in this section.

The acoustoelectric effect and the associated amplification has beenpreviously utilized in surface acoustic wave (SAW) devices which haslimitations in terms of operation frequency (loosing efficiency athigher frequencies), low electromechanical coupling (very lowefficiency).

What is needed is a new system that overcomes such limitations.

SUMMARY

The below summary is merely representative and non-limiting.

The above problems are overcome, and other advantages may be realized,by the use of the embodiments.

In a first aspect, an embodiment provides an apparatus foracoustoelectric amplification. The apparatus includes a semiconductorlayer and a thin piezoelectric layer bonded or deposited onto thesemiconductor layer forming an acoustic cavity. Two or more tethersforming a current conduction path through the semiconductor layer andtwo or more access pads to silicon are positioned on two ends of theacoustic cavity and configured to inject a DC current in thesemiconductor layer.

In another aspect, an embodiment provides a further apparatus foracoustoelectric amplification. The apparatus includes a semiconductorlayer having a current isolation trench defining a suspended filterstructure. A thin piezoelectric layer is bonded or deposited onto thesemiconductor layer and together they form an acoustic cavity within thesuspended filter structure. The apparatus also includes pairs ofinterdigital transducers (IDT) configured to excite and detect radiofrequency signals within the suspended filter structure. Two or moreaccess pads to silicon are positioned on two ends of the acoustic cavityand are configured to inject a DC current in the semiconductor layerwithin the suspended filter structure.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

Aspects of the described embodiments are more evident in the followingdescription, when read in conjunction with the attached Figures.

FIG. 1 shows a schematic of the device shows the electrode configurationfor lateral field excitation (LFE) as well as points of electricalcontact to Si; inset visualizes AE interaction of piezoelectric fieldand electrons in the device.

FIG. 2 shows theoretical and experimental insertion loss (IL) of thetargeted device for different voltages (bottom)/currents (top).

FIG. 3 shows a frequency response of the device for different injectedcurrents from 0 μA to 150 μA showing improvement in loss and qualityfactor (Q) as the current increases.

FIG. 4 is a scanning electron micrograph (SEM) picture of the devicedesigned for AE amplification.

FIG. 5 shows a schematic of an embodiment having a stack cross-sectionand FEA simulated frequency response.

FIG. 6 shows a SEM of an A-type filter and other IDT designs.

FIG. 7 demonstrates a measured frequency response of an A-type filterbefore and after passing 500 μA of current.

FIG. 8 demonstrates a measured frequency response of S₂₁(S₁₂) [shown insolid(dashed)] of a D-type filter for a 0 to 400 μA current sweep,displaying the switchablity of the device.

FIG. 9 demonstrates a measured transmission/isolation response of four(4) other types of the filters.

FIG. 10 illustrates a summary of the measured AE gain and NTR of thefilters as a function of current (and applied drift field) showing NTRsmore than 20 dB.

FIG. 11 illustrates a schematic of an embodiment having current injectedin the Si layer, AE interactions result in non-reciprocity with respectto the direction of electron flow (dashed arrow).

FIG. 12 shows a SEM of ADL200 with its corresponding electricalconnections; the inset shows the close up view of the IDTs having 5 μmfinger pitch.

FIG. 13 demonstrates the frequency response of ADL200 measured prior tocurrent injection (left) while the ports are terminated to 50Ω and(right) the terminations are conjugate match of the ports of the device.

FIG. 14 shows the frequency response of ADL200 and ADL200R where thedark curves correspond to I_(DC)=0 μA and the grey ones to T_(DC)=150μA; solid and dashed lines are respectively S₂₁ and S₁₂.

FIG. 15 shows the frequency response (|S₂₁| on the left and |S₁₂| on theright) of ADL400 terminated to 50Ω for increasing the I_(DC) from 0 to400 μA.

FIG. 16 demonstrates the IL measured from the peak S₂₁ and S₁₂ ofdifferent ADL types measured for different values of I_(DC) showing alarger AE gain in ADL400.

FIG. 17 demonstrates the analytical curves for the acoustoelectricamplification coefficient (a) for different values of the applied driftfield and free carrier concentrations for the LNoSi ADL (such as shownin FIG. 11 ).

FIG. 18 demonstrates the current generated by the acoustic wavespropagating in the device.

DETAILED DESCRIPTION OF THE INVENTION

This patent application claims priority from U.S. Provisional PatentApplication No. 62/876,268, filed Jul. 19, 2019, the disclosure of whichis incorporated by reference herein in its entirety.

Utilizing the AE effect in a piezoelectric-semiconductor resonant cavitycan overcome the limitations in the conventional technology, in part, byamplifying bulk acoustic waves in a structure with highelectromechanical coupling that was not feasible in the past andintroduce a new paradigm for transistor-less amplification at both lowerand higher frequencies and non-reciprocal devices.

The AE effect is the generation of electrical signal in response toacoustic wave (or vice versa). Amplification creates a higher signalamplitude, “gain”. Resonant Cavities are structures that confineacoustic vibrations in the MHz-THz range (for RF applications) and theelectrical and mechanical properties of the piezoelectric-semiconductorcavities can be tuned by independently choosing the proper materialsthat are employed in such devices.

Acoustic waves propagating in a piezoelectric medium are accompanied bya coupled electric field due to the piezoelectricity. In a thinpiezoelectric film this field can penetrate into the surroundings andinteract with charge carriers present within a certain distance. As aresult, in a composite structure consisting of a thin layer ofpiezoelectric and semiconductor an energy exchange process existsbetween the propagating acoustic waves and the charge carriers in thesemiconductor, from the former to the latter, leading to a lossmechanism called AE loss.

By pumping energy into the semiconductor layer through applying anelectric field across it—so that the velocity of charge carriers exceedthat of the acoustic wave, energy transfer can be reversed (from thecharge carriers to the acoustic waves) leading to the amplification ofthe acoustic waves. Such phenomenon can be employed in various devicesand configurations that consist of a thin stack of piezoelectric layeron a semiconductor layer such as TPoS (thin-film piezoelectric-on-Si)resonators, filters, delay lines, oscillators, etc. This is realized byplacing (depositing or bonding) a layer of piezoelectric material incontact with a semiconductor substrate with proper doping concentrationand forming the desired acoustic cavity and applying an electric fieldin parallel with the direction of acoustic wave propagation in thesemiconductor layer. The described scheme can be used for buildingnon-reciprocal amplifiers without utilizing active circuit components,near-zero insertion loss filters that eliminate the need for amplifierstages, oscillators, circuit-less quasi-passive wireless sensors withlong detection range and duration of signal transmission, duplexers,isolators, and circulators. One of the more important features of theacoustoelectric amplification is that as the frequency of operationincreases, the achievable gain increases too, exactly the opposite ofamplification mechanism in transistor-based amplifiers where thegain-frequency product is limited.

Evidence for AE amplification in lateral-extensional TPoS resonantcavities is demonstrated. Due to the piezoelectric coupling, anevanescent electromagnetic wave is induced in the silicon (Si) layerthat is a part of the resonant cavity, exchanging momentum with thecarriers. Therefore, by injecting an electric current in this layer, theacoustic equivalent of Cherenkov radiation—AE amplification—can berealized. Such phenomenon is observed in a 1 GHz TPoS resonant cavity inwhich lateral field excitation (LFE) is utilized to excite the acousticwave.

The acoustoelectric (AE) effect, a bi-directional coupling between theacoustic waves and electron flow (e.g., current) in a piezoelectricsemiconductor (such as Cadmium Sulfide), fascinated a generation ofphysicists and engineers for decades during the 20th century. A majorimplication of the AE phenomena is AE amplification of traveling bulkacoustic waves (BAW)—and later pseudo-standing due to round-trip gain inacoustic masers—using an induced DC current.

This effect has a specific criterion over relative acoustic velocity andelectron drift velocity. It turns out such a condition renders the AEamplification quite inefficient in common piezoelectric semiconductors.An alternate proposal places a high mobility semiconductor substrateadjacent to a good piezoelectric substrate such that the electric fieldassociated with the acoustic wave traveling in the piezoelectricsubstrate penetrates into the semiconductor. As such, structures inwhich a semiconductor such as silicon (Si) is held in close proximity ofa Lithium Niobate (LN) substrate where surface acoustic waves (SAW) areexcited and detected were proposed, yielding limited success andefficiency.

The rise of gallium nitride (GaN) as a suitable candidate forhigh-electron mobility and power transistors, once more, invigoratedresearch in AE interactions, leading to demonstration of gain in BAW GaNfilters, for instance. Moderate carrier concentration—improving carriermobility and reducing the adverse effect of carrier diffusion—and highelectromechanical coupling are essential for AE gain. By separating thepiezoelectric and semiconductor media, these two can be chosen andadjusted independently, improving the overall amplification performance.AE gain can be realized in thin-film piezoelectric-on-silicon (TPoS)resonant devices by injecting a DC current through the Si layer.High-order lateral-extensional TPoS resonant cavities operating at 1 GHzare chosen for proving the feasibility of this concept.

A stack of 1 μm (20%) scandium doped aluminum nitride(Sc_(0.2)Al_(0.8)N)—having twice the electromechanical coupling of pureAlN (0.4% herein) while being compatible with CMOS processing—sputteredon 2 μm of lightly doped n-type Si (in the order of 1E14 cm⁻³) forms theacoustic cavity. The electrode configuration for this resonant device ismodified compared to the previous typical design as the bottom metal isremoved to facilitate penetration of electric fields between thepiezoelectric and the semiconductor layers (see FIG. 1 ). Instead, thetop metal layer is redesigned to enable lateral field excitation (LFE)of the harmonic lateral-extensional resonance mode at around 1 GHz. LFEis used to ensure the electric field due to the piezoelectricity in theScAlN layer penetrates into the Si layer and exchanges momentum with thecarriers within. Two extra pairs of tethers are added to the structurethat form a current conduction path through the Si layer. Two accesspads to silicon are also opened up on the two ends of the cavity throughwhich a DC current is injected in the silicon. The DC contacts areisolated from the rest of the substrate to largely limit the currentpath through the resonant cavity.

FIG. 1 shows a schematic of the device showing the electrodeconfiguration for LFE as well as points of electrical contact to Si aslabeled by DC1 and DC2; inset conceptually visualizes AE interaction ofpiezoelectric field and electrons in the device. The device isfabricated on ScAlN on silicon on insulator substrate where the SiO2layer serves as the sacrificial layer for releasing the device. Theinterdigital transducers are made of Mo and the electrical contacts toSi are overlayed with Ti for improving electrical contact. The processfor producing acoustoelectric amplification in lateral-extensional thinfilm piezoelectric-on-silicon (TPoS) resonant cavities is describedbelow. Acoustic waves are excited by applying an RF signal between RF1and GND, acoustoelectric gain is achieved by injecting a DC current (DC)through the Si layer and the acoustic signal is detected by reading thesignal from RF2 and GND. Potential products include: unilateralamplifiers, zero loss filters, oscillators, high detection rangecircuit-less wireless sensors and other acoustic wave devices (e.g.,duplexers, circulators, isolators). A 0.23 dB gain has been realizedwith preliminary predictions showing a 50 dB gain possible.

In order to achieve an expression for the AE attenuation of compositeresonant devices, the boundary condition corresponding to the set ofequations for electric and elastic fields in both media are equated attheir interface. This results in a dispersion equation for the systemthat can be modified and applied to standing wave devices as well toobtain the incremental gain due to AE effect:

$\begin{matrix}{\alpha = {K^{2}{{G\omega}\left( {\frac{\eta - 1}{\begin{matrix}{\left( {\eta - 1} \right)^{2} +} \\{C^{2}\left( {1 + {\omega^{2}\text{/}\omega_{C}\omega_{D}}} \right)}^{2}\end{matrix}} + \frac{\eta + 1}{\begin{matrix}{\left( {\eta + 1} \right)^{2} +} \\{C^{2}\left( {1 + {\omega^{2}\text{/}\omega_{C}\omega_{D}}} \right)}^{2}\end{matrix}}} \right)}}} & (1)\end{matrix}$

Here K is the electromechanical coupling, η is ratio of electronvelocity (V_(e)) to acoustic velocity (V_(a)), ω_(c)=qμN/ε_(si) andω_(D)=qV_(a) ²/k_(B)Tμ are the carrier relaxation and diffusionfrequency respectively, G=ε_(si)dω_(c)[tgh(βd/βd]/2ε_(ScAlN)V_(a) ², andC=qμNd[tgh(βd)/βd]/ε_(ScAlN)V_(a) a where d is thickness of the Silayer, N is the free carrier concentration, β is the wave propagationconstant, T is the temperature, k_(B) is Boltzmann constant, and q iselementary charge. By separating the AE attenuation coefficient from theother sources of loss (α_(total)=α_(other)+α_(AE)) the insertion loss(IL) can be written in the following form:

$\begin{matrix}{{{IL}({dB}\;)} = {20{\log_{10}\left( \frac{A_{0}e^{- \alpha}{other}^{- \alpha}{{AE}\begin{pmatrix}{{\cos\left( {{\omega t} + {\beta z}} \right)} +} \\{\cos\left( {{\omega t} - {\beta z}} \right)}\end{pmatrix}}}{A_{0}\left( {{\cos\left( {{\omega t} + {\beta z}} \right)} + {\cos\left( {{\omega t} - {\beta z}} \right)}} \right)} \right)}}} & (2)\end{matrix}$

Hence, the term due to the AE loss can be isolated so that the rightside of the equation simplifies to sum of IL at no DC current and theelectric gain due to the current injection (3).

$\begin{matrix}{{20{\log_{10}\left( e^{\alpha_{AE}} \right)}} + {20{\log_{10}\left( \frac{A_{0}e^{\alpha}ot{her}^{\alpha}{{AE}\begin{pmatrix}{{\cos\left( {{\omega t} + {\beta z}} \right)} +} \\{\cos\left( {{\omega t} - {\beta z}} \right)}\end{pmatrix}}}{A_{0}\left( {{\cos\left( {{\omega t} + {\beta z}} \right)} + {\cos\left( {{\omega t} - {\beta z}} \right)}} \right)} \right)}}} & (3)\end{matrix}$

By substituting the measured IL at no DC current in the right side termof (3) and the calculated electric gain from (1) in the left side term,the expected IL is derived and plotted in FIG. 2 for different appliedvoltages; the theoretical (connected by a dashed line) and experimental(connected by a solid line) IL of the targeted device for differentvoltages (bottom)/currents (top) are shown in FIG. 2 .

While measuring the frequency response (e.g., S₂₁) of the targeteddevice using a Rohde & Schwarz ZNB 8 network analyzer and a pair ofCascade Microtech GSG probes at room temperature in atmosphericpressure, a DC probe is used to apply a DC voltage across the pair of Sielectrical contacts and injected current is measured. The average IL ofthe device as a function of the applied voltage is plotted in FIG. 2(data points are connected by solid line), showing a 0.23 dB gain bypassing a ˜150 μA current which is less than the 0.48 dB expected fromthe theory that can be possibly due to adverse effect of joule heatingin the device. The frequency response of the resonator with increasingthe current is plotted in FIG. 3 and the SEM picture of the device isshown in FIG. 4 .

Using AE amplification in lateral-extensional TPoS overcomes issues withthe transistor-based amplifiers available today which all suffer fromthe limited gain-frequency product meaning that as the frequencyincreases, the gain decreases and reaches zero. Acoustoelectricamplification mechanism, on the other hand, becomes more efficient andoffers higher gains as the frequency increases. Filtering networksintroduce attenuation to the signal and require additional amplifyingstages with active components while a resonant filter functioning withthis scheme can be tuned to introduce no loss to the signal or amplifythe signal. Sensors that offer long detection range require beingaccompanied by active circuits that are size and cost ineffective. Thecircuit-less quasi passive sensors, however, offer long detection rangeand transmission duration with addition of a small battery.Non-reciprocal delay-lines with zero insertion-loss can be realizedusing such phenomenon.

High gain unilateral amplifiers, resonant filters with zero loss,self-amplifying filters and oscillators, and long-range non-complexsensors all can be realized and are crucial for today's communicationdevices, especially due to the trends of internet of things,miniaturization, closely spaced narrow communication bands, and lowpower consumption. For instance, various embodiments can potentiallyreplace the power-hungry amplifier stages in communication networkswhile consuming a power in the range of 100 μW or less.

Amplifiers and filters that incorporate the acoustoelectricamplification have the potential to substitute the conventionaltransistor-based amplifiers that are widely used today in many differentelectrical devices. The fast pace growth in the internet of things (IoT)sector requires cheap sensors with long detection ranges where theaforementioned sensors can perfectly fit in.

An embodiment provides an apparatus for acoustoelectric amplification.The apparatus includes a semiconductor layer and a thin piezoelectriclayer deposited/bonded onto the semiconductor layer and forming anacoustic cavity. At least two tethers forming a current conduction paththrough the semiconductor layer are present. The apparatus also includesat least two access pads DC1 and DC2 disposed in a Titanium (TI) regionin the silicon and positioned on two ends of the acoustic cavity. Theseat least two access pads DC1 and DC2 are configured to inject a DCcurrent in the semiconductor layer.

In a further embodiment of the apparatus above, the thin piezoelectriclayer comprises 1 (20%) scandium doped aluminum nitride(Sc_(0.2)Al_(0.8)N), and the semiconductor layer comprises 2 of lightlydoped n-type Si. The materials and thicknesses used are not limited tothe aforementioned ones; Aluminum nitride (which can be scandium doped),lithium niobate, gallium nitride, etc. can be used as the piezoelectriclayer, having a thickness of a few nano meters to a few microns.Additionally, the semiconductor layer can be Si, Ge, compoundsemiconductors such as III-V materials, graphene, etc., provided thatthey have the proper carrier concentration and mobility.

In another embodiment of any one of the apparatus above, the at leasttwo access pads are configured to inject the DC current so as to applyan electric field in parallel with a direction of acoustic wavepropagation in the semiconductor layer.

Further embodiments enable operation as MEMS filters and delay lineswith more than ˜20 dB of nonreciprocity and ˜6 dB gain. This, forinstance, can potentially be implemented in the radio frequency frontends (RFFE) as the fifth generation (5G) and beyond uses full-duplexcommunications, that is most efficiently achieved by non-reciprocal andadaptive filters and long but miniaturized and low-loss delays.

In the 5G and beyond era in telecommunications, a great number of issuesrise up that are crucial to address. Among them are the limitedavailable frequency spectrum for data communication, interference fromthe transceiver module (self-interference) and from the overly congestedelectromagnetic spectrum (external-interference). This is because 5Grelies on a great number of transceivers and antennas in the closevicinity of one another along with the additional traffic due to theinternet of things (IoT) to build the communication network as a whole.As a result, full-duplexed communication along with interferencemitigation architectures are inevitable as it enables doubling thecommunication capacity through simultaneous transmission and receive atthe same frequency. Such a scheme, however, mandates integration ofnon-reciprocal components which are currently unavailable as the currentRFFE modules are entirely implemented based on inherently reciprocalplatforms. While using ferromagnetic components, material nonlinearity,or some time-varying electronic approaches have been suggested, theyeither suffer from miniaturization and integration issues, frequencyconversion, high power consumption, or highly complex architectures(e.g., need for external clocks, switches, etc.).

Another area of interest is the tactical communications field that usesfrequency selective limiters for non-reciprocal suppression of highpower in-band signals that can saturate and disable the receivers, hencehindering the tactical connectivity. The possibility of miniaturizednon-reciprocal components based on the AE effect may be used only a fewmilliwatts of power consumption which can potentially circumvent theabove-mentioned issues and become a ubiquitous component in the novelcommunication architectures.

On the other hand, recently in the optoelectronics field, time-reversalsymmetry has proven to be avoidable by employing the interaction betweenphotons and acoustic phonons. This opens up possibilities of controllingthe light propagation, achieving optical gain (laser and its bandwidthnarrowing), microscopy, and material characterization. However, in orderto achieve such, a high power laser is required to induce large acousticvibrations in the structure which decreases the efficiency andpracticality of this scheme. Through the AE interactions, electronscould assist in inducing larger vibrations and consequently relaxing thepower requirements of the utilized laser.

A non-limiting embodiment provides a demonstration of bulk-mode lithiumniobate-on-silicon (LNoSi) nonreciprocal transversal filters thatexploit the acoustoelectric (AE) effect for signalamplification/attenuation. In these devices, a direct current is passedthrough the underlying Si layer to adjust the insertion loss (IL) andnonreciprocal transmission ratio (NTR) of the device. AE gains up to 5.6dB with >20 dB NTR are obtainable by injecting ˜500 μA of current. Thisallows for merging filters, switches, and tunable attenuators in aminiaturized device which is a sought-after stepping stone forfacilitating full-duplexed communications.

The AE effect, e.g., momentum exchange between electrons and acousticphonons, ignited a great deal of research during the 20^(th) centurywith the goal of developing surface acoustic wave (SAW) amplifiers andsignal processors. However, success was limited by the existingfabrication capabilities, discouraging researchers from furtherinvestigations. The recent demonstrations of the AE effect, from theobservation of a DC current associated with acoustic waves in epitaxialAlGaN/GaN delay lines to a gain in LN/semiconductor SAW structures, isdue to the advances in thin film growth and bonding techniques. Here,such effect is utilized to demonstrate bulk-mode LNoSi transversalfilters with large tunable gains and nonreciprocity.

To satisfy the requirements for maximum AE coupling, e.g., highelectromechanical coupling and low concentration of high-mobilityelectrons, an X-cut LN wafer is

directly bonded to a lightly (˜7E14 cm⁻³) n-type doped (100) SOI waferwhere the SiO2 layer acts as the sacrificial layer for releasing thedevice and forming the suspended structure. The wafers are oriented sothat the 30° off +y-axis plane of LN (that offers the highest couplingfor symmetric Lamb waves) is aligned to the [110] Si plane (see FIG. 5). Twenty (20) pairs of interdigital transducers (IDT) at the two portsRF1 and RF2 (respectively defined by RF1 and GND and RF2 and GND pairs)allow for lateral-field excitation/detection of RF signal as the bottomelectrode is avoided to promote AE interactions. The IDT is made of Moand its finger pitch (FP) determines the center of the pass-band. Thelateral boundary of the suspended filter (labeled by L and A) is definedby etching the device stack. This also restricts the current to passthrough only the underlying Si body upon biasing the Au overlaidopenings of Si. The RF signal can be amplified (or attenuated) from oneport RF1, RF2 to another depending on the intensity and the direction ofelectron drift with respect to the traveling acoustic waves, resultingin nonreciprocity and switchability.

Table 1 summarizes the design parameters, IL, and fractional bandwidth(FBW) of the filters. The effect of device length (L), aperture (A), andelectrode configuration (e.g., bidirectional or regular, split, andlinearly swept FP) are studied. The SEM of an A-type filter and all theelectrode configurations is displayed in FIG. 6 .

TABLE 1 Types of the filters with their performance Device Type A B C DE F IDT Type Swept Reg. Reg. Reg. Reg. Split L (μm) 100 200 200 400 400400 A (μm) 150 150 200 150 200 150 FP (μm) 5 to 6 5 5 5 5 5 IL (dB) 15.416.5 17.3 19.3 21.6 25.8 FBW (%) 2.8 2.1 2.3 1.6 1.9 2.7

The filters are characterized at normal temperature and pressure (NTP)by a VNA and calibrated GSG probes while a controlled current isinjected through the filters with DC probes. The RF characteristic of anA-type filter before (black) and after (grey) passing a 500 μA currentis shown in FIG. 7 . The IL and reverse isolation are enhanced and anNTR of 4.9 dB is achieved. The same for a D-type filter for a currentsweep from 0 to 400 μA is shown in FIG. 8 . While the FBW is smallerthan that of the A-type, a 5.6 dB gain and 19.9 dB NTR is achieved,virtually turning off the reverse transmission. The S₂₁/S₁₂ of all theother filters and the summary of the measured AE gains and NTRs areshown in FIGS. 9 and 10 , respectively. The results presented high AEgain can be achieved in bulk-mode AE devices with much lower powerconsumption compared to the recent SAW counterparts. This suggests thepossibility of developing fully-switchable near-zero IL filters throughfurther design optimizations.

A major implication of the AE amplification in this scheme is theselective amplification that applies almost exclusively to the pass bandof the device. This is in stark contrast with the transistor basedamplification scheme in which signal amplification occursnon-selectively or “blindly” and is only limited by gain x bandwidthproduct. In other words, only the acoustic modes supported by the devicethat meet the AE amplification criteria are amplified. This togetherwith proper mode isolation techniques could enable amplification schemesin which signal-to-noise ratio (SNR) is preserved or even improved. FIG.18 shows the generation of an AE current (I_(AE)) almost exclusivelywithin the device pass band which translates into the energy couplingbetween the drifting electrons and acoustic signals only at the passband of the device. For this task, the RF port of the device is excitedas the frequency is swept and the current generated by acoustic waves isrecorded from the DC contacts. Generation of this AE current almostexclusively within the device pass band enables frequency selectiveamplification.

Another embodiment provides lithium niobate-on-silicon (LNoSi)non-reciprocal acoustic delay lines (ADL) with tunable insertion loss(IL) utilizing the acoustoelectric (AE) effect. Due to the AE effect,the direction- and the intensity-dependent momentum exchange between thedrifting electrons in the Si layer and the acoustic phonons can beutilized to break the intrinsic reciprocity of the ADLs in order tocontrol their frequency response. A 5.2 dB improvement in the IL and a14.2 dB increase in the reverse isolation (e.g., a 19.4 dBnon-reciprocal transmission ratio) is achieved through injecting a 400μA current in one of the ADLs presented here. This opens uppossibilities of merging long delays, tunable attenuators, and switchesin a single miniaturized device which is a critical stepping stone infulfillment of full-duplexed microwave systems.

While the revolution in electronics mainly relied on silicon (Si) and itcontinues to be driven by it, lithium niobate (LN) is playing the samerole in the integrated photonics field. As a result, hybridelectro-optic devices will likely be realized on LN on Si (LNoSi)heterogeneous platforms. Furthermore, due to its outstandingpiezoelectric properties, LN has been long studied and employed in radiofrequency (RF) acoustics for signal processing applications. Morespecifically, a great deal of research on the acoustoelectric (AE)phenomenon was fueled once LN-semiconductor heterostructures werepreceded by piezoelectric semiconductor materials as the testbed forstudying such phenomenon in the 1960s. The AE effect was initiallyobserved in the form of the attenuation of acoustic phonons in anelectron plasma as a result of the momentum transfer from former tolatter; eventually, it was employed in surface acoustic wave (SAW) AEamplifiers by drifting electrons faster than the phase velocity of theacoustic waves (AW) in a manner similar to a travelling-wave-tubeamplifier. However, limited fabrication capabilities at the time andsubsequently devices with low efficiency discouraged many researchersfrom further investigations.

It was until recently that advances in wafer-level bonding enabled newdemonstrations of the AE effect in heterogeneous SAW structures based onLN while our group demonstrated such effect in thin-filmpiezoelectric-on-Si (TPoS) Lamb wave resonators. The AE interactions inthe latter comprises the piezoelectric coupling as well as thedeformation potential, both of which contribute to the anharmonicelectron bunching due to the stress in the piezoelectric film and Silayer, respectively. Utilizing such interactions in LNoSi platformenable realization of non-reciprocal Lamb wave acoustic delay lines(ADL) that concurrently allow for tuning the insertion loss (IL) andswitching. In this scheme, the inherent reciprocity of such componentsis broken by the drifting electrons in the underlying Si layer; as itamplifies the signals (e.g., AW) propagating in its direction whileattenuating those that propagate in the opposite direction. Suchcapabilities in a single miniaturized component facilitate theimplementation of full-duplexed communications and mitigation ofinterference in the congested RF spectrum, both of which are essentialto the 5G and beyond networks.

FIG. 11 illustrates a schematic of an embodiment having current injectedin the Si layer, AE interactions result in non-reciprocity with respectto the direction of electron flow (dashed arrow).

In order to maximize the AE interactions, a high electromechanicalcoupling in conjunction with a low concentration of high mobilityelectrons is desired. To satisfy such conditions, an X-cut LN wafer isdirectly bonded to a lightly n-type doped 4-inch (100) SOI wafer. TheSiO2 layer of SOI wafer acts as the sacrificial layer for forming thesuspended device structure. The wafers are oriented so that the 30° off+y-axis plane of LN that is commonly known to offer the highest couplingfor the symmetric Lamb waves is aligned to the [110] plane of the Siwhich allows for the highest electron mobility. The device structure isschematically displayed in FIG. 11 . The device stack consists of 1 μmLN and 3 μm Si at a doping level of ˜7E14 cm⁻³.

Lamb waves are launched by means of 20 pairs of interdigital transducers(IDT) made of a 100 nm thick molybdenum (Mo) layer from one port (RFapplied between RF1 and GND) and detected at the second port (RF readacross RF2 and GND) after propagating through the delay region. Byutilizing the lateral field excitation, the device structure may omit abottom electrode. This allows for the strong penetration of thepiezoelectrically coupled electric fields into the Si layer andguarantees stronger AE interactions once a DC is applied to the Si layervia the Au overlaid contact points.

The IDT finger pitch, defined as the center to center distance betweentwo consecutive electrodes, determines the center of the ADL pass-bandand is chosen to be 5 μm in this non-limiting embodiment. The freedom inthe IDT pattern which spatially maps the frequency pass band of the ADLcan be used to accommodate a variety of pass band responses (e.g.,narrow-band, wide-band). The length of the delay region determines theinsertion delay (ID) as well as the amount of AE gain andnon-reciprocity. Delay lengths of 200 μm (ADL200) and 400 μm (ADL400)are demonstrated below which respectively correspond to 30 ns and 60 nsreal-time ID. Longer delay lengths correspond to longer real time delay,for instance a real time delay of ˜0.6 ns can be expected in a ADLhaving 4 mm of delay length.

The lateral boundary of the device is defined by etching the devicestack which also restricts the current to pass only through the ADL.In-plane acoustic reflectors are incorporated in one of theconfigurations (ADL200R) to illustrate its effect. In order to passcurrent through the underlying Si, contacts are formed by etching the LNfilm and depositing gold (Au) and the ADL is suspended by etching thebackside handle layer. The scanning electron micrograph (SEM) of afabricated device and its IDT is shown in FIG. 12 , a SEM of ADL200 withits corresponding electrical connections; the inset shows the close upview of the IDTs having 5 μm finger pitch.

The current values passing through the device are demonstrated sincethey directly impact the AE interactions. By doing so, the parasiticeffects of non-Ohmic junctions between Au and lightly n-Si is mostlyavoided.

Depending on the current intensity and direction, the propagating AWscan be attenuated or amplified along the ADL from one port to anotherwith the AE gain (G_(AE)) expression beingG _(AE) =e ^(αL)  (4)where α is the incremental gain coefficient, and L is the device length.The incremental gain is generally expressed in the form of

$\begin{matrix}{{\alpha\text{/}k_{0}} = {\frac{K^{2}}{2}\frac{\gamma\omega\tau}{1 + \left( {\gamma\omega\tau} \right)^{2}}}} & (5)\end{matrix}$where k₀ and ω are the wavenumber and angular frequency, K² is theelectromechanical coupling, y is the relative difference between theelectron drift velocity and AW phase velocity, and i is a time constantthat is determined by the conductivity and permittivity of thestructure. It can be inferred from Eq. (4) that the longer the ADL, themore AE gain and subsequently loss compensation is achievable. Thisdirectly translates to longer ID with lower IL; as the AE gainovercompensates for the propagation loss which has been reported to be˜1 dB·mm⁻¹ in such class of LN ADLs while Si is a very low acoustic lossmaterial, as well.

FIG. 17 demonstrates the analytical curves for the acoustoelectricamplification coefficient (a) for different values of the applied driftfield and free carrier concentrations for the LNoSi ADL (such as shownin FIG. 11 ).

The devices are characterized at normal temperature and pressure by avector network analyzer using ground signal ground (GSG) microprobesafter performing on chip short-open-load-thru calibration to move thereference plane to the microprobe tips. Meanwhile, a pair of DC probesare used to feed the ADL with a voltage source with a controlled current(I_(DC)). FIG. 13 shows the measured frequency response (magnitude ofthe S-parameters) of ADL200 terminated to 50Ω (left) and a conjugatelymatched load (right) prior to passing I_(DC). The ADL shows reciprocityand the fractional bandwidth (FBW) is measured to be 2.1% while the ILis 19.2 dB and 16.5 dB before and after performing the single stage lowpass LC matching using the Keysight ADS software, respectively.

FIG. 14 shows the frequency response of ADL200 and ADL200R where thedark curves correspond to I_(DC)=0 μA and the grey ones to I_(DC)=150μA; solid and dashed lines are respectively S₂₁ and S₁₂.

Next, I_(DC) is passed through the ADLs while their RF characteristicsis measured. The IL is improved once the electron drift is in the samedirection as the propagating RF signal while the reverse isolation isalso enhanced due to the AE attenuation of backscattering waves. FIG. 14compares the magnitude of S₂₁ and Su of the ADL200 and ADL200R beforeand after passing I_(DC)=150 μA through them. While the S₂₁ and S₁₂overlap without passing the current, such amount of current results in anon-reciprocal transmission ratio (NTR=|S₂₁|/|S₁₂|) of 5.3 dB and 2.7dB, respectively. Terminating the ADL with the acoustic reflectorimproves the IL at the expense of reducing the attainable NTR.

FIG. 15 shows the frequency response (|S₂₁| on the left and |S₁₂| on theright) of ADL400 terminated to 50Ω for increasing the I_(DC) from 0 to400 μA. The transmission and reverse isolation of ADL400 are shown asthe injected current is increased. The IL and NTR of the ADL is tunableby changing the I_(DC), yielding a 5.2 dB enhancement in the IL with a19.4 dB of NTR at I_(DC)=400 μA. Additionally, with reversing thecurrent flow, the direction of the changes in the S₂₁ and S₁₂ isreversed and the ADL is virtually switched off at such current. Themeasured peak S₂₁ and S₁₂ of the devices studied herein for a currentsweep from 0 to 250 μA is plotted in FIG. 16 , confirming that a largerAE gain and NTR is achievable in the longer ADL.

An additional knob for fine-tuning the AE gain is available by applyinga bias to the top IDTs and take advantage of themetal-insulator-semiconductor capacitor that is inherently formed in thedisclosed structures. By applying the bias to the IDTs, thesemiconductor layer (Si herein) can be depleted from charge carriers oraccumulated. Such carrier density variations allow for adjusting the AEgain and non-reciprocity independent from the main bias voltage that isused for carrier drift. This additionally allows for compensating thevariations of the carrier concentration from the values targeted in thedesign as a result of perturbations for example during the wafer bondingor etc.

By using the momentum exchange between the acoustic phonons andelectrons, e.g., acoustoelectric effect (AE), in lithium niobate onsilicon heterostructures, various embodiments can enable non-reciprocalLamb wave acoustic delay lines (ADL) that can provide long delays withswitching capabilities in a single miniaturized device. By passing adirect current through the lightly doped Si layer, the insertion loss(IL), reverse isolation, and non-reciprocal transmission ratio (NTR) ofthe ADLs can be manipulated and at a constant current, a higher tuningrange for the IL and NTR is achievable for longer devices.

The foregoing description has been directed to particular embodiments.However, other variations and modifications may be made to the describedembodiments, with the attainment of some or all of their advantages.Modifications to the above-described systems and methods may be madewithout departing from the concepts disclosed herein. Accordingly, theinvention should not be viewed as limited by the disclosed embodiments.Furthermore, various features of the described embodiments may be usedwithout the corresponding use of other features. Thus, this descriptionshould be read as merely illustrative of various principles, and not inlimitation of the invention.

What is claimed is:
 1. An apparatus for acoustoelectric amplification,the apparatus comprising: a semiconductor layer; a thin piezoelectriclayer bonded onto a top surface of the semiconductor layer and formingan acoustic cavity; at least two radio frequency (RF) signal accessports (RF1 and RF2), electrically coupled to the thin piezoelectriclayer, each of the at least two RF signal access ports including aplurality of interdigital transducers (IDTs) formed by a plurality ofinterdigital fingers, each of the plurality of interdigital fingerscoupled to one of the at least two RF signals access ports (RF1 and RF2)and ground (GND), and configured to input and detect RF signals withinthe thin piezoelectric layer forming said acoustic cavity; and at leasttwo DC current coupling pads (DC1 and DC2), electrically coupled to thesemiconductor layer and electrically isolated from the at least two RFsignal access ports (RF1 and RF2), and configured for coupling to asource of DC current, the at least two DC current coupling pads (DC1 andDC2) configured for injecting a DC current form the source of a DCcurrent into the semiconductor layer.
 2. The apparatus of claim 1,wherein the thin piezoelectric layer comprises at most 1.5 μm lithiumniobate (LiNbO3) and the semiconductor layer comprises at most 3 μm oflightly doped n-type silicon (Si).
 3. The apparatus of claim 1, whereinthe at least two DC current coupling pads are configured to inject theDC current mainly in parallel with a direction of acoustic wavepropagation in the semiconductor layer.
 4. An apparatus foracoustoelectric amplification, the apparatus comprising: a semiconductorlayer; a thin piezo-electric layer deposited onto the semiconductorlayer and forming an acoustic cavity; at least two tethers forming acurrent conduction path through the semiconductor layer; and at leasttwo access pads electronically coupled to the semiconductor layerwherein at least one of the at least two access pads is electricallyisolated from at least one radio frequency (RF) access port, therebylimiting the current conduction path through the semiconductor layer. 5.The apparatus of claim 4, wherein the thin piezoelectric layer comprisesat most 1.5 μm lithium niobate (LiNbO3) and the semiconductor layercomprises at most 3 μm of lightly doped n-type Si.
 6. The apparatus ofclaim 4, wherein the at least two access pads are configured to injectthe DC current mainly in parallel with a direction of acoustic wavepropagation in the semiconductor layer.
 7. An apparatus foracoustoelectric amplification, the apparatus comprising: a semiconductorlayer having a current isolation trench, the current isolation trenchconfigured for confining current in a suspended structure; a thinpiezoelectric layer, bonded onto the semiconductor layer and forming anacoustic cavity within the suspended structure; a plurality of pairs ofinterdigital transducers (IDT), disposed on the thin piezoelectric layerforming the acoustic cavity, and configured to excite and detect radiofrequency signals within the thin piezoelectric layer forming theacoustic cavity; and at least two access pads, electrically coupled tothe semiconductor layer and positioned on two ends of the cavity andconfigured for coupling to a DC current source, and configured to injecta DC current in the semiconductor layer within the suspended acousticcavity.
 8. The apparatus of claim 7, wherein the plurality of pairs ofIDTs are configured to result in unidirectional acoustic wavegeneration.
 9. The apparatus of claim 7, wherein a physical distanceforming a physical separation between a first input and a second outputinterdigital transducer pair of the plurality of pairs of interdigitaltransducers define at least one acoustic delay line (ADL) within thesuspended structure.
 10. The apparatus of claim 9, wherein the at leasttwo access pads are configured to inject the DC current into the atleast one ADL.
 11. The apparatus of claim 7, wherein the semiconductorlayer is a lightly n-type doped (100) SOI wafer.
 12. The apparatus ofclaim 7, wherein the plurality of pairs of IDTs comprise one of amolybdenum (Mo), gold or aluminum layer.
 13. The apparatus of claim 12,wherein the molybdenum (Mo), gold or aluminum layer is approximately 50to 200 nm thick.
 14. The apparatus of claim 7, wherein the plurality ofpairs of IDTs have a finger pitch that is at least equal to thethickness of the suspended structure.
 15. The apparatus of claim 7,wherein the plurality of pairs of IDTs are separated by a physicaldistance defining a delay region, forming a traveling wave filter. 16.The apparatus of claim 15, wherein the delay region comprises a lengthof at least 200 μm to at most 4 mm.
 17. The apparatus of claim 7,wherein the apparatus is configured to receive separate bias voltages tothe plurality of pairs of IDTs in order to modify carrier concentrationin the semiconductor layer, enabling adjusting of acoustoelectricamplification and nonreciprocity.